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    • Mercury's model of rotation: the short periodic terms

    Paper number

    IAC-06-A3.P.2.02

    Author

    Mr. Julien Dufey, Facultés Universitaires Notre-Dame de la Paix Namur, Belgium

    Coauthor

    Prof. Anne Lemaître, Facultés Universitaires Notre-Dame de la Paix Namur, Belgium

    Coauthor

    Mrs. Sandrine D Hoedt, Facultés Universitaires Notre-Dame de la Paix Namur, Belgium

    Year

    2006

    Abstract
    Mercury has been an important field of research these past few years. In addition to its unique 3:2 spin-orbit resonance in the solar system, in 2004 the NASA launched the space mission MESSENGER and the ESA and ISAS are planning their BepiColombo mission for 2012.
In this paper we study the rotation of Mercury for a relatively short time scale (10 to 50 years). Long-period models have already been made, but the innovation here is that we introduce the effects due to the short periodic terms, so that the model is valid for a space mission time scale.
The rotation is studied in a hamiltonian formalism. We use a model developped by D’Hoedt and Lemaitre in 2004 as basis. In this model we consider that Mercury has a keplerian orbit, that the resonance is taken into account as well as the non-sphericity of the planet (mainly flattening of the poles) and the precession of the node.
With this Hamiltonian, taking into account the effects mentionned above, we apply an averaging process based on Lie perturbation theory. This is supposed to average the Hamiltonian so that the terms periodic in mean anomaly vanish. With the help of the generator derived from this averaging process, we are able to write the time evolution of the variables. We can actually write a relation between the averaged variables and the non-averaged ones. The most important results are the variation of the obliquity and the resonant angle when we place Mercury at the exact equilibrium.
For the computations we constantly use an algebraic manipulator called MSNam and the programs are implemented in Fortran 90.
The amplitude of the different oscillations are pretty small, but as Mercury is not at the exact equilibrium, these amplitudes grow when we move the planet away from this equilibrium.
We are also currently working on higher orders of the Lie averaging process and on introducing a non-keplerian orbit for Mercury, i.e. a model where we consider the direct planetary perturbations based on the ephemeris of the IMCCE of Paris.
    Abstract document

    IAC-06-A3.P.2.02.pdf

    Manuscript document

    IAC-06-A3.P.2.02.pdf (🔒 authorized access only).

    To get the manuscript, please contact IAF Secretariat.